Abstract. 1 Introduction

Transcription

1 Simulation supported design ofliga microsystems K.-R Kamper, J. Dopper,W. Ehrfeld, B. Hagemann, S.D.J. Hill, H.Lehr IMM Institute of Microtechnology GmbH, Carl-Ziess-Strafie 18-20, D Mainz-Hechtsheim, Germany Abstract Recent progress in the maturation of LIGA technology with its large inherent potential for the cost-effective mass fabrication of complex microstructures, has led to an increased commercial interest for microproducts. The use of modern computer simulation tools to achieve competitive development cycle times and optimum technical performance is one of the essential prerequisites for the successful development of marketable and application suitable microsystems. In this paper examples for the use of simulation tools for the optimisation of various microsystems are presented, including the use of electromagnetic analysis software, flow modelling and simulation of the injection moulding process. The results clearly indicate the advantages to be gained by the application of sophisticated modelling software in the field of microtechnology. 1 Introduction Computer simulations are presently gaining importance in almost all technical fields. The well-known reasons include the ubiquitous need for shorter development cycle times, reduced development costs and enhanced product performance, as well as the ever increasing complexity of technical products. The state of maturity reached by current simulation software permits the replacement of common trial-and-error techniques by the systematic and reliable optimisation of critical product components. Similar arguments are especially relevant for the development of microsystems. The comparatively large initial costs for the application of advanced microstructuring techniques, like LIGA, combined with the relatively long iteration intervals due to the multiple number of essential technological process

2 4 Microsystems and Microstructures steps do not allow a cost effective development cycle including the fabrication of several prototypes. The need for computer simulations becomes ever more pronounced for the design of microproducts, since certain physical and chemical effects, e.g. involving the role of surfaces, gain in importance with decreasing dimensions. The physical intuition of the design engineer, which plays a crucial but often underestimated role in the development process of technical products, usually does not properly account for the physical effects dominating in micro dimensions. Furthermore the actual measurement of physical quantities inside miniaturised systems is rendered increasingly difficult with decreasing dimensions. Computer simulations help to visualise the results of physical phenomena in the microworld, and hence are a valuable tool for gaining physical insight into the behaviour of miniaturised physical and technical systems. A number of simulation tools have been applied in the past, mainly for the design of mechanical systems. The advent and success of LIGA technology pushes the demand for advanced simulation tools in another dimension.^ Due to the huge variety of materials available for use in the LIGA technique, which are specifically adapted to the need of the sensing or action to be performed, optimised designs are now possible. This includes a full 3-D realisation of microstructures made from different components by use of function adapted materials like polymers for optical purposes, specific metals with low resistance to guide the electrical current or magnetic materials. It is the purpose of this paper to illustrate the use of various simulation tools for the design of microsystems by the consideration of typical examples. ball bearing shaft permanent magnet coil system return yoke electrical connection Figure 1: Schematic design of an electromagnetic micromotor 2 Electromagnetic micromotor Reliable electromagnetic micromotors with dimensions in the millimetre range, long lifetimes and the capability to deliver torque in the unm range and revolution speeds of some rpm are required for an increasing number of applications, namely in the field of medical technology.^ The optimisation of the performance of such micromotors and their adaptation to specific applications

3 Microsystems and Microstructures 5 requires the use of sophisticated electromagnetic design tools, such as the software package OPERA/TOSCA by VECTORFIELDS, which has been used for the following calculations. One possible design for electromagnetic micromotors is illustrated in Figure 1. A diametrically magnetised cylinder, fabricated out of a high performance permanent magnet material, rotates inside a tube-shaped softmagnetic return yoke. The electromagnetic excitation is generated by a coil system located inside the air gap between permanent magnet and return yoke. Since a major design goal concerns the optimisation of the torque delivered by the micromotor, the magnetic induction B inside the magnetic system is one of the most interesting quantities. The small dimensions require an extremely efficient use of the magnetic materials, e.g. the application of magnetic induction values close to saturation. Figure 2 compares the absolute value of the magnetic induction for two different motor geometries. A quarter of the distribution of the magnetic induction across a cut through the middle of the micromotor is shown for a fairly optimum geometry on the left, while the results on the right have been calculated for a less efficient geometry with an undersized return yoke. Since the air gap is kept the same for both configurations, the diameter of the permanent magnet is larger for the case depicted on the right side. The magnetisation direction of the permanent magnet can be easily inferred from the high induction values in the air gap. Across the air gap the well-known 1/r fall-off of B can be recognised. Inside the yoke the highest induction values are reached perpendicular to the magnetisation direction of the permanent magnet, since all the magnetic flux lines captured by the return yoke have to pass through this part of the yoke. Figure 2: Magnetic induction B across a cut through the middle of a micromotor (left side: yoke thickness 150 pm, right side: yoke thickness 50 pm) The magnetic induction in the thicker yoke is below saturation everywhere. In contrast an extended part of the thinner yoke is fully saturated, i.e. this yoke is not able to properly guide the magnetic flux anymore. The torque which can

4 6 Microsystems and Micro structures be delivered by the motor is proportional to the integrated magnetic flux through the air gap. Although the permanent magnet on the right side has a large diameter the total flux through the gap is about 10% smaller than the flux in the left configuration. Thus in contrast to general anticipation the configuration with the smaller permanent magnet exhibits the larger torque. This clearly demonstrates the necessity to optimise the different geometrical parameters simultaneously. Microelectromechanical systems often exhibit air gaps, which in relation to the dimensions of the magnetic components are rather large compared to their macroscopic counterparts. Thus stray fields and edge effects need to be considered very carefully and in many cases turn out to be quite significant. Proper simulation of such effects often requires the application of true 3D-modelling. An example illustrating the importance of edge effects in microelectromechanical systems is shown in Fig. 3, which displays the component of the magnetic induction normal through a cylinder in the middle of the air gap of the above described micromotor. This normal component essentially determines the torque. The region at the edges of the rotor with a significant reduction of the normal magnetic induction amount to approx. 15 % of the total rotor length. Normal component of B (T) Figure 3: Normal component of the magnetic induction across the middle of the airgap of an electromagnetic micromotor 3 Microfluidic Valve Fluidic microsystems, such as miniaturised chemical analysis systems or micro reactor systems, need a variety of different micro valves. Microfluidic valve structures without any moving parts are very attractive, since they are much less sensitive to a possible contamination of the fluid by particles than, e.g., membrane valves. One type of such fluidic valves consists of a nozzle/diffuser structure, exhibiting a flow direction dependent flow resistance. The functional

5 Microsystems and Microstructures 7 principle of such valves essentially relies on turbulent behaviour of the fluid at the end of the nozzle. Since flow behaviour usually gets more laminar upon increasing miniaturisation, it is difficult to judge the behaviour of microfluidic structures from the empirical know how on macroscopic valve structures. We therefore simulated the flow behaviour of a miniaturised nozzle / diffuser structure by the software FLOTRAN by COMPUFLO. Typical flow lines for the forward and the backwards direction are shown in Figure 4. Figure 4: Geometry of microfluidic valve and typical flow lines (Left: Forward direction, Right: Backwards direction, Bottom: Detail of the flow directly behind the nozzle end) Somewhat surprisingly such afluidicstructure exhibits a smaller flow resistance for flow in the diffuser direction, compared to the flow resistance for flow in the nozzle direction. This is caused by the generation of large eddy currents behind the nozzle, which absorb a substantial amount of the kinetic energy of the fluid. For flow in the diffuser direction one observes smooth laminar flow, indicating a smaller flow resistance for this flow direction. Inside a nozzle with a typical width of 20 jum and a heigth of 300 jam the calculation yields Reynolds numbers on the order of 100 despite the small dimensions. For flow rates below 1 ml / min differences of 20 % between the forward and backwards direction are observed. The results clearly indicate further miniaturisation of this valve type to result in even lower efficiencies, i.e. to be of no practical use. In contrast to the diffuser/nozzle valve membrane valves can be miniaturized without any functional deficiencies. A membrane valve essentially consists of two chambers separated by a thin membrane, which is perforated in the middle. The performance of this kind of valve is critically influenced by the geometry of the valve seat, which determines, for example, the tension of the membrane in the closed state. The optimisation of such valves necessarily involves FEM calculations, since the well-known analytical models are only valid for rather small deflections. The stress inside the membrane exhibits the highest values close to the border of the membrane and can easily surpass critical values. Computer modelling has been applied sucessfully in order to

6 8 Microsystems and Microstructures predict the stress in membrane valves and to find geometric configurations with sufficiently low stress values. Proper rounding of the border of the membrane can lower the stress by approximately 30 %. 4 Micro-pump In this last example computer simulation is used to optimise the design of a microsystem with respect to the feasibility and ease of its fabrication by micro injection moulding. Simple fill and cool analyses have recently been embellished with options that automatically balance runner systems and optimise the design of gates and cooling lines. It is relatively straightforward to manipulate a comprehensive set of process parameters with the aim of reducing cycle times, selecting suitable moulding materials or avoiding problems with the warp and shrinkage of parts. Modelling the moulding of a specific part can provide a detailed insight into the filling characteristics of the mould which, for example, can be used to control the formation of weld-lines or to avoid regions that induce high shear stresses and so-called "hot spots". We have applied the modelling software I-DEAS Master Series Thermoplastic Moulding version 1.3c by SDRC to simulate the micro-injection moulding process for the design of components of a micro-pump. A schematic of this type of micro-pump is shown in Fig. 5. The pump modelled features a thin membrane of 100 urn thickness and a diameter of 5.5 mm. Three tube connectors represented by the three thin lines (two horizontal and one vertical) have diameters of approximately 200 um (see Fig. 7). The simulations were used to determine a minimum thickness values for the membrane and to find a configuration that avoided premature freezing of the melt inside a partially filled tube-connector. Top Membrane Bottom Figure 5: Schematic design of a micro-pump It can be seen from Fig. 6 that the melt flows around the thin membrane and does not begin to fill it until after the main plate has been filled. The pressure then rises abruptly and the membrane starts to fill. This particular simulation

7 Microsystems and Microstructures 9 resulted in a short-shot, showing that under the conditions used, the membrane has to be thicker than 100 um. However, the tube connectors are seen to be completely filled. Previous simulations had shown that if the connectors would be positioned too close to the gate inlet, plastic entering the connectors would immediately slow and quickly drop in temperature to below the no-flow temperature of the melt resulting in partially filled connectors. Fill Time /sec Figure 6: Fill-time sequence for the moulding of a micro-pump component Peak Temperature / C Figure 7: Temperature profile at a given time-step during the filling of the micro-pump mould

8 10 Microsystems and Microstructures Fig. 7 shows the temperature profile of the part at a given instant in the filling process. It can be seen, that the melt heats up due to viscous heating as it surges through the constrictions which lead to the membrane and tube connectors. These constrictions were designed so that the micro-pump could be broken away from the main-plate. The hottest temperature of the plastic is seen to be just seven degrees higher than the injection temperature (320 C) which is perfectly acceptable. 5 Conclusions The results of this work demonstrate the potential and the necessity of computer simulation tools for the design and optimisation of microsystems. In many cases modelling reveals results somewhat unanticipated by intuition, which, however, are crucial to the performance of the microsystem investigated. The examples given could easily be extended to a large variety of other fields in microtechnology, such as micro-optics and components for chemical and biological micro-reactors. Current simulation software can in many cases yield sufficient insight into the physical behaviour of a microsystem to allow for a systematic optimisation. However, it is essential for the design engineer to know about the limits of the models behind the simulation tools and to critically judge any simulation result. Since current software developed for the simulation of macroscopic systems does not always take into account all physical effects of significance in the microworld, development work is necessary to complete and optimise the existing packages. Acknowledgement This work was partially supported by the European Union through BriteEuRam project no. BE7838. S. Hill gratefully acknowledges the role of the European Union in supporting this work through a Human Capital and Mobility Fellowship, contract number: ERB CHB GCT Ehrfeld, W.; Lehr, H. Advanced microstructure products by synchrotron radiation lithography, Journal de Physique, Vol. 4, p. C C9-236, LefBmollmann, Chr. Fertigungsgerechte Gestaltung von Mikrostrukturen fur die LIGA-Technik, Dissertation, University of Karlruhe, Lehr, H.; Abel, S.; Ehrfeld, W.; Hagemann, B.; Kamper, K.-P.; Michel, F.; Thurigen, Ch. Assembly of Electromagnetic Milliactuators with LIGA Components, Proceedings of the 2nd Japan-France congress on Mechatronics, Nov. 1-3, Takamatsu, Kagawa, Japan, 1994